Partition of the spectra for the lower triangular double band matrix as generalized difference operator Δv over the sequence spaces c and lp (1 < p <∞)


Proyecciones, cilt.39, ss.51-71, 2020 (Diğer Kurumların Hakemli Dergileri) identifier


© Universidad Catolica del Norte.Let the sequence (vk) is assumed to be either constant or strictly decreasing sequence of positive real numbers satisfying limk∞ vk = L > 0 and supk vk ≤ 2L. Then the generalized difference operator Δv is Δvx = Δv(xn) = (vnxn - vn-1xn-1)n=0∞ with X-1 = v-1 = 0. The aim of this paper is to obtain the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Δv and modified of the operator Δv; on the sequence spaces c and lp(1 < p <∞).